Tessellations - Mathematics, Art, and Recreation

This book aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. It covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Also includes special topics like spiral tilings and tessellation metamorphoses.

List of contents

1. Introduction to Tessellations. 2. Geometric Tessellations. 3. Symmetry and Transformations in Tessellations. 4. Tessellations in Nature. 5. Decorative and Utilitarian Tessellations. 6. Polyforms and Reptiles. 7. Rosettes and Spirals. 8. Matching Rules, Aperiodic Tiles, and Substitution Tilings. 9. Fractal Tiles and Fractal Tilings. 10. Non-Euclidean Tessellations. 11. Tips on Designing and Drawing Escheresque Tessellations. 12. Special Techniques to Solve Design Problems. 13. Escheresque Tessellations Based on Squares. 14. Escheresque Tessellations Based on Isosceles Right Triangle and Kite-Shaped Tiles. 15. Escheresque Tessellations Based on Equilateral Triangle Tiles. 16. Escheresque Tessellations Based on 60°-120° Rhombus Tiles. 17. Escheresque Tessellations Based on Hexagonal Tiles. 18. Decorating Tiles to Create Knots and Other Designs. 19. Tessellation Metamorphoses and Dissections. 20. Introduction to Polyhedra. 21. Adapting Plane Tessellations to Polyhedra. 22. Tessellating the Platonic Solids. 23. Tessellating the Archimedean Solids. 24. Tessellating Other Polyhedra. 25. Tessellating Other Surfaces.

About the author

Robert Fathauer has had a life-long interest in art but studied physics and mathematics in college, going on to earn a PhD from Cornell University in electrical engineering. For several years he was a researcher at the Jet Propulsion Laboratory in Pasadena, California. Long a fan of M.C. Escher, he began designing his own tessellations with lifelike motifs in the late 1980s. In 1993, he founded a business, Tessellations, to produce puzzles based on his designs. Over time, Tessellations has grown to include mathematics manipulatives, polyhedral dice, and books.
Dr. Fathauer's mathematical art has always been coupled with recreational math explorations. These include Escheresque tessellations, fractal tilings, and iterated knots. After many years of creating two-dimensional art, he has recently been building ceramic sculptures inspired by both mathematics and biological forms. Another interest of his is photographing mathematics in natural and synthetic objects, particularly tessellations. In addition to creating mathematical art, he's strongly committed to promoting it through group exhibitions at both the Bridges Conference and the Joint Mathematics Meetings.

Summary

This book aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. It covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Also includes special topics like spiral tilings and tessellation metamorphoses.

Additional text

"A treasure trove of geometric delights, this book will draw you into the beautiful and deep questions of mathematics that come from the simple question of how shapes fit together."– Edmund Harriss, University of Arkansas and the co-author of Patterns of the Universe: A Coloring Adventure in Math and Beauty

"A beautifully presented, comprehensive introduction to tessellations––what tessellation enthusiasts and teachers (at all levels) have wished for. The author, a talented tessellations artist himself, captures the fascination of tessellations through beautiful color illustrations. His chapters touch on every aspect of tessellations—their history, the many different types, where they occur, their symmetries, ways in which they are classified, their practical uses. More than half of the book is devoted to thoughtful advice and careful descriptions of how to create various kinds of tessellations. Questions and activities (often with helpful worksheets or templates) throughout are useful not only for teachers and students, but for anyone who wishes to test their understanding. This is truly an indispensible book for all those who want to learn about, teach, or make tessellations."– Doris Schattschneider, Recipient of Mathematical Association of America's Carl B. Allendoerfer Award and the author of M.C. Escher Kaleidocycles

"Fathauer's book is a fun, accessible, and lavishly illustrated guide to the universe of tessellations. You can study the structure of tessellations, and even learn to make your own. It's certain to appeal to anyone who wants to explore this beautiful topic at the intersection of art and mathematics."– Craig Kaplan, University of Waterloo

"A gorgeously illustrated romp through tiling theory, a pleasure to read and fun for all ages and levels and a must for every geometry classroom and geometry buff’s bookshelf!– Chaim Goodman-Strauss, University of Arkansas and the co-author of The Symmetries of Things

Product details

• Authors: Robert Fathauer
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 31.10.2020
• EAN: 9780367185978
• ISBN: 978-0-367-18597-8
• No. of pages: 464
• Series: AK Peters/CRC Recreational Mathematics Series
• Subjects: Natural sciences, medicine, IT, technology > Mathematics; MATHEMATICS / Applied, MATHEMATICS / History & Philosophy, MATHEMATICS / Geometry / General, Mathematics, geometry, Philosophy of Mathematics, Applied mathematics